How to Size a Portable Generator for Home Use

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Portable Generators are a reliable source of power in the absence of utility power. They provide electrical power to supply our critical power needs when the utility company is unable to supply us electrical power due to fault in their transmission system or during maintenance interventions in their power infrastructure or in the worst case of a natural disaster such as earthquake or a hurricane that has destroyed section of the power grid.

What Size of Portable Generator Do I need ?

The size of portable generator you need depends on your power requirement when the need arises to use the generator. Do you require the generator to power all of your electrical appliances at once? Or do you require the generator to power some critical electrical load during power outage? The bigger your power needs, the bigger the size of your generator and the more expensive your portable generator will be!

Running Watts of an Electrical Appliance

The running watts of an electrical appliance is the power it can draw continuously with rated voltage and current. It is usually calculated as:

Running Watts = Rated Voltage x Rated Current.

Note that the above formula will give power in volts-amps or VA but assuming a power factor = 1 which is rarely the case, we get power in watts. This approximation is done to enable easy sizing of a portable generator for home use.

The running watt can easily be calculated by using the rated voltage and current on the name plate of the appliance. Generators are also rated for their running watts. It is the power the generator can deliver continuously at rated voltage, current and frequency. A generator must not be made to continuously carry load beyond its running watts for a very long time otherwise the generator’s life will be shortened and the device becomes damaged in a short time.

Surge Watts or Start up Power of an Electrical Appliance

Certain devices and appliances have an electric motor or compressor in them. They require additional watts to start them. This additional watt may also be referred to as the surge watt of the device. The surge watts required by these devices may sometimes be two or three times the watts required to run the device. Heat producing devices also called resistive loads such as light bulbs, toasters or coffee makers do not require surge watts at start up. A generator must have enough surge watts capacity to handle devices that require surge watts at start up to prevent a nuisance tripping of the main power breaker in the generator.

As shown above, a generator must have sufficient surge capacity to carry loads requiring additional power during start up. Consider a refrigerator that works for one third of the time within a given time cycle. Each time the refrigerator compressor starts, a generator powering the refrigerator must have sufficient surge power for the compressor each time it comes on!

How to Calculate the Size of Portable Generator Required

To properly size a generator, care should be taken to analyse the load the generator is to power so that both running watts and surge watts can be correctly calculated. To calculate the size of generator:

Add up the total running and surge watts for each appliance. Multiply the total sum gotten by a contingency of 15 – 20 % to get the capacity of your generator.

As a guide during the sizing calculation for domestic application;

Surge watts for refrigerators and air conditioners = 2 x running watts 

Surge watts for motors (surface or submersible pumps) = 3 x running watts

Microwave Oven = 1.5 x running watts

Sample Sizing Calculation

Suppose the following loads are to be powered by a portable generator:

Electrical Load	Number	Running Watts (W)
Refrigerator	1	800
Submersible pump	1	800
Lighting loads	lot	150
Air Conditioner (1hp)	1	800
Deep Freezer	1	500
Microwave	1	600
Computer	1	300
TV	1	400

Determine power rating for generator  as shown below:

Electrical Load	Number	Running Watts (W)	Surge Watts (W)
Refrigerator	1	800	2 x 800 = 1,600
Submersible pump	1	800	3 x 800  = 2,400
Lighting loads	lot	150	0
Air Conditioner (1hp)	1	800	2 x 800 = 1,600
Deep Freezer	1	500	2 x 500 = 1,000
Microwave	1	800	1.5 x 800 = 1200
Computer	1	300	0
TV	1	400	0
Total		4,350	7,800
Total Power Required	= 4,350 + 7,800 = 12,150W
Add 15% contingency	= 12,150 x 1.15 =13,972.5W
Size of Generator needed			= 15,000W or 15KVA   standard Size

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How to Calculate Inverter Power Rating and Inverter Battery Backup Time

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Inverter systems are a common feature in our homes and workplace where they play a prominent role in the ensuring uninterruptible power to sensitive loads and devices. For home applications, there is the need to adequately size your inverter to be able to meet the expected load demand. 

Inverters convert DC voltage to AC voltage. They have a battery system which provide adequate backup time to provide continuous power in the home. The inverter system then converts the battery voltage to AC voltage through electronic circuitry. The inverter system also has some charging system that charges the battery during utility power. During utility power, the battery of the inverter is charged and at the same time power is supplied to the loads in the house. When utility power fails, the battery system begins to supply power via the inverter to the loads in the home as shown below:

How to Size and Calculate the Inverter Power Requirement

Inverter power is rated in VA or KVA.

Power in VA = AC Voltage x AC Current in Amps

Power in KVA = AC Voltage x AC Current in Amps/1000

Power in Watts = AC Voltage x AC Current in Amps x PF

Where PF = power factor 

Power in KW = AC Voltage x AC Current in Amps x PF/1000

Also  Power in W = Power in VA x PF

         Power in KW = Power in KVA x PF

Suppose we want to size an inverter to carry the following loads:

1. Lighting load, 300W

2. 3 Standing fans of 70W, each

3. 2 LCD TV, 100W

4. 1 Home Theatre Music System, 200W

5. 1 Juice extractor, 150W

Applying Power in KW = Power in KVA x PF

Power in KVA  = Power in KW/PF = Power in KW/0.8    (Nominal PF = 0.8, which is standard for homes)

Total load in Watts = 300 + (3 x 70) + 200 + 200 + 150 = 1060W = 1.06KW

Power in KVA = 1.06/0.8 = 1.325

An inverter of standard rating 1.5KVA is required to carry the loads above.

How to Calculate Inverter Battery Backup Time

The backup time for batteries in an inverter system depends on the number of batteries as well as their capacity in Amp-hours.

Inverter battery backup time is calculated as:

Back up time = Battery Power in Watt hour (Wh)/Connected Load in Watts (W)

Battery Power in Wh = Battery Capacity in AH x Battery Voltage (V) x Number of Batteries

Let us shorten the formula by using the following Symbols:

Let BUT = battery backup time in hours

            C = battery capacity in AH 

    V = battery voltage in volts

    N = Number of batteries in series or parallel as the case may be.

    $P_L$ = connected load in watts (W)

Now

$$BUT = {\frac{C*V*N}{ P_L}}$$

In our example above, suppose we have selected a 24V, 1.5KVA inverter system that is to use two 12V batteries in series connection and suppose further that the capacity of our batteries are 200AH each, then :

C = 200AH

V = 12V

N = 2

$P_L$   = 1,060W

$$BUT = {\frac{200 * 12 * 2}{1060}} = 4.53 hrs$$

How UPS (Uninterruptible Power Supply) Systems Works

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UPS stands for Uninterruptible Power Supply. A UPS system is an autonomous source of alternate power that is used to supply sensitive electronic loads such as computer centers, telephone exchanges and many industrial-process control and monitoring systems. These applications require power that is availability and of good quality.

A UPS solution for sensitive electrical loads is used to provide a power interface between the utility and the sensitive loads, providing voltage that is:

1. Free of all disturbances present in utility power and in compliance with the strict

        tolerances required by loads.

2. Available in the event of a utility outage, within specified tolerances

UPS systems satisfy requirements in 1 & 2 above in terms of power availability and quality by:

1. Supplying loads with voltage complying with strict tolerances, through use of an

        inverter

2. Providing an autonomous alternate source, through use of a battery

3. Stepping in to replace utility power with no transfer time, i.e. without any interruption in the               supply of power to the load, through use of a static switch.

These characteristics make UPS units the ideal power supply for all sensitive applications because they ensure power quality and availability, whatever the state of utility power.

Basic Parts of a UPS System

A UPS comprises the following main components:

1. Rectifier/charger, which produces DC power to charge a battery and supply an inverter

2. Inverter, which produces quality electrical power free of all utility-power disturbances, notably           micro-outages and that is within tolerances compatible with the requirements of sensitive                     electronic devices.

3. Battery, which provides sufficient backup time to ensure the safety of life and property by                   replacing the utility as required

4. Static switch, a semi-conductor based device which transfers the load from the

        inverter to the utility and back, without any interruption in the supply of power

Types of Static UPS Systems

Types of static UPSs are defined by standard IEC 62040. The standard distinguishes three operating modes for UPSs which are:

1. Passive standby (also called off-line)

2. Line interactive

3. Double conversion (also called on-line)

These definitions concern UPS operation with respect to the power source including the distribution system upstream of the UPS. IEC Standard 62040 defines the following terms:

a. Primary power: power normally continuously available which is usually supplied by

        an electrical utility company, but sometimes by the user’s own generation

b. Standby power: power intended to replace the primary power in the event of

        primary-power failure

c. Bypass power: power supplied via the bypass

UPS Operating in Passive Standby Mode

Operating Principle:

The inverter is connected in parallel with the AC input in a standby as shown below:

UPS in Passive Standby Mode. Photo Credit: Schneider Electric

Normal Mode Operation

In normal mode operation, the load is supplied by utility power via a filter which eliminates certain disturbances and provides some degree of voltage regulation (IEC 62040 specifies some form of power conditioning). The inverter operates in passive standby mode.

Battery Backup Mode Operation

In battery backup mode operation, when the AC input voltage is outside specified tolerances for the UPS or the utility power fails, the inverter and the battery step in to ensure a continuous supply of power to the load following a very short less than 10 ms transfer time. The UPS continues to operate on battery power until the end of battery backup time or the utility power returns to normal, which causes transfer of the load back to the AC input (normal mode).

Application

This configuration is a compromise between an acceptable level of protection against disturbances and cost. It can be used only with low power ratings less than 2 kVA.

Limitations

This UPS operates without a real static switch, so a certain time is required to transfer the load to the inverter. This time is acceptable for certain individual applications, but

incompatible with the performance required by more sophisticated, sensitive systems

(large computer centers, telephone exchanges, etc.). Furthermore, the frequency is not regulated and there is no bypass.

UPS Operating in Line-interactive Mode

The inverter is connected in parallel with the AC input in a standby configuration, but also charges the battery. It thus interacts with the AC input source as shown below:

UPS in Line-interactive Mode. Photo Credit: Schneider Electric

Normal Mode Operation

In normal mode operation, the load is supplied with conditioned power via a parallel connection of the AC input and the inverter. The inverter operates to provide output-voltage conditioning and/or charge the battery. The output frequency depends on the AC-input frequency.

Battery Backup Mode Operation

In this mode of operation, when the AC input voltage is outside specified tolerances for the UPS or the utility power fails, the inverter and the battery step in to ensure a continuous supply of power to the load following a transfer without interruption using a static switch which also disconnects the AC input to prevent power from the inverter from flowing upstream. The UPS continues to operate on battery power until the end of battery backup time or the utility power returns to normal, which provokes transfer of the load back to the AC input (normal mode).

Bypass Mode Operation

This type of UPS may be equipped with a bypass. In the bypass mode, If one of the UPS functions fails, the load can be transferred to the bypass AC input (supplied with utility or standby power, depending on the installation).

Application and Limitation

This UPS configuration is not well suited to regulation of sensitive loads in the medium to high-power range because frequency regulation is not possible. For this reason, it is rarely used other than for low power ratings.

UPS Operating in Double Conversion (On-line) Mode

Operating Principle:

In this type of UPS, the inverter is connected in series between the AC input and the application as shown below:

UPS in Double-Conversion Mode. Photo Credit: Schneider Electric

Normal Mode Operation

During normal operation, all the power supplied to the load passes through the rectifier/charger and inverter which together perform a double conversion (AC to DC to AC), hence the name.

Battery Backup Mode Operation

In battery backup mode, When the AC input voltage is outside specified tolerances for the UPS or the utility power fails, the inverter and the battery step in to ensure a continuous supply of power to the load following a transfer without interruption using a static switch. The UPS continues to operate on battery power until the end of battery backup time or utility power returns to normal, which causes transfer of the load back to the AC input (normal mode).

Bypass Mode Operation

This type of UPS is generally equipped with a static bypass, sometimes referred to as a static switch. The load can be transferred without interruption to the bypass AC input (supplied with utility or standby power, depending on the installation), in the event of UPS failure, load current transient (inrush or fault currents) or load peaks. The presence of a bypass assumes that the input and output frequencies are identical and if the voltage levels are not the same, a bypass transformer is required.

For certain types of load, the UPS must be synchronized with the bypass power to ensure load-supply continuity. Furthermore, when the UPS is in bypass mode, a disturbance on the AC input source may be transmitted directly to the load because the inverter no longer steps in. Another bypass line, often called the maintenance bypass, is available for maintenance purposes. It is closed by a manual switch.

Common Causes of Battery Failures

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All batteries have a limited life span. However the life span can be considerably shortened by certain factors which tend to cause premature battery failure. The factors discussed below are some of the most common causes of battery failure. Given the roles batteries play and will continue to play in our everyday life, a thorough understanding of these factors will enable engineers and technicians involved in the maintenance of batteries prevent the occurrence of some of these factors in order to prolong battery life.

The factors discussed below are mostly applicable to VRLA (Valve Regulated Lead Acid) batteries which have almost completely replaced conventional lead acid batteries with refillable liquid sulphuric acid electrolyte. VRLA batteries are designed to be maintenance free and the hydrogen that is emitted is recombined internally so that the electrolyte (essentially a paste) does not need replacing over the life of the battery, a valve is installed to release any excess pressure that may build up if the battery were failing. A key drawback of VRLA batteries is the short service life which was procured at the expense of low maintenance.

Elevated Temperatures

Anticipated battery life is specified by the manufacturer for batteries installed in an environment at or near the reference temperature of 25°C (77°F). Above this temperature, battery life is reduced. The chief aging mechanism is accelerated corrosion of the positive plates, grid structure, and strap, which increases exponentially as a function of temperature. Elevated temperatures reduce battery life. An increase of 8.3°C (15°F) can reduce lead-acid battery life by 50% or more. 

Repeated Cycling

Repeated cycling from fully charge to fully discharge and back may cause loss of active materials from the positive plates. This reduces battery capacity and its useful life.

Overcharging

Overcharging by the battery charging system causes excessive gassing and high internal heat. Too much gassing can lead to the removal of active material from the plates. Too much heat can also oxidize the positive plate material and warp the plates.

Undercharging

A faulty charging system will not maintain the battery at full charge. Severe undercharging allows sulfate on the plates to become hard and impossible to remove by normal charging. The undercharged battery may fail to deliver the required power needed for its application.

Over discharge

Over discharge leads to hydration. Hydration occurs in a lead-acid battery that is over discharged and not promptly recharged. Hydration results when the lead and lead compounds of the plates dissolve in the water of a discharged cell and form lead hydrate, which is deposited on the separators. When the cell is recharged, multiple internal short circuits occur between the positive and negative plates. Once hydration is evident, the cell is permanently damaged. Hydration is not visible in VRLA cells because the containers are opaque

Vibration

A battery must be mounted securely. Vibrations can loosen connection, crack the case and damage internal components.

DC Ripple Current

Excessive DC ripple current might contribute to battery aging. VRLA batteries are extremely susceptible to ripple current since it can lead to cell heating and will accelerate the degradation of cells which are at risk from thermal runaway.

Improper Storage

Storing wet cells beyond the manufacturer’s recommended duration promotes sulfation, and decreases cell capacity and life.

Misapplications

Batteries are commonly designed for a specific use. If the battery is not designed for a given application, it might not meet its life or performance expectations.

Understanding Battery Technical Specifications.

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Commonly in a specification sheet for a typical battery, you have all kinds of technical terms that need to be understood so as to be able to use the battery in the right way to get maximum benefit from  the battery in a particular application. Summarized below are some of the key technical terms used in battery specifications:

Nominal Voltage (V)

This is the reference voltage of the battery, also sometimes thought of as the “normal” voltage of the battery.

Cut-off Voltage (V)

This is the minimum allowable voltage of a battery. It is this voltage that generally defines the “empty” state of the battery.

Capacity or Nominal Capacity (AH for a specific C rate)

This is the total Amp-hours available when the battery is discharged at a certain discharge current (specified as a C-rate) from 100 percent state-of-charge to the cut-off voltage. Capacity is calculated by multiplying the discharge current (in Amps) by the discharge time (in hours) and decreases with increasing C-rate.

State of Charge (% SOC)
SOC is defined as the remaining capacity of a battery and it is affected by its operating conditions such as load current and temperature. It is calculated as:

$$  SOC  = {\frac {Remaining \ Capacity}{Rated \ Capacity}} $$

Depth of Discharge
DOD is used to indicate the percentage of the total battery capacity that has been discharged.

$$ DOD = 1 - SOC $$

Energy or Nominal Energy (Wh for a specific C rate)

This is the “energy capacity” of the battery, the total Watt-hours available when the battery is discharged at a certain discharge current (specified as a C-rate) from 100 percent state-of-charge to the cut-off voltage. Energy is calculated by multiplying the discharge power (in Watts) by the discharge time (in hours). Like capacity, energy decreases with increasing C-rate.
The rated Wh capacity of a battery can be calculated as:

$Rated \ Wh = Rated \ Ah \ Capacity \ * \ Rated \ Battery \ Voltage$

Cycle Life (Number for a specific DOD)

This is the number of discharge-charge cycles the battery can experience before it fails to meet specific performance criteria. Cycle life is estimated for specific charge and discharge conditions. The actual operating life of the battery is affected by the rate and depth of cycles and by other conditions such as temperature and humidity. The higher the DOD, the lower the cycle life.

Specific Energy (Wh/Kg)

This is the nominal battery energy per unit mass, sometimes referred to as the gravimetric energy density. Specific energy is a characteristic of the battery chemistry and packaging. It is expressed in Watt-hours per kilogram (Wh/kg) as:

$$Specific \ Energy = {\frac {Rated \ Wh \ Capacity}{Battery \ Mass \ in \ Kg}}$$

Specific Power (W/Kg)

This is the maximum available power per unit mass. Specific power is a characteristic of the battery chemistry and packaging. It determines the battery weight required to achieve a given performance target. It is expressed in W/kg as:

$$Specific \ Power = {\frac {Rated \ Peak \ Power}{Battery \ Mass \ in \ Kg}}$$

Peak Power
The peak power of a battery is defined as:
$$P = {\frac{2V_{oc}^2}{9r}}$$
Where:
$V_{oc}$ is the open circuit voltage of battery
$r$ is the internal resistance of the battery

Energy Density (Wh/L)

This is the nominal battery energy per unit volume, sometimes referred to as the volumetric energy density. Specific energy is a characteristic of the battery chemistry and packaging. Along with the energy consumption of the vehicle, it determines the battery size required to achieve a given electric range.

Power Density (W/L)

The maximum available power per unit volume. Specific power is a characteristic of the battery chemistry and packaging. It determines the battery size required to achieve a given performance target.

Maximum Continuous Discharge Current

This is the maximum current at which the battery can be discharged continuously. This limit is usually defined by the battery manufacturer in order to prevent excessive discharge rates that would damage the battery or reduce its capacity. 

Maximum 30-sec Discharge Pulse Current

This is the maximum current at which the battery can be discharged for pulses of up to 30 seconds. This limit is usually defined by the battery manufacturer in order to prevent excessive discharge rates that would damage the battery or reduce its capacity.

Charge Voltage (V)

This is the voltage that the battery is charged to when charged to full capacity. Charging schemes generally consist of a constant current charging until the battery voltage reaches the charge voltage, then constant voltage charging, allowing the charge current to taper until it is very small.

Float Voltage (V)

This is the voltage at which the battery is maintained after being charge to 100 percent SOC to maintain that capacity by compensating for self-discharge of the battery.

(Recommended) Charge Current

The ideal current at which the battery is initially charged (to roughly 70 percent SOC) under constant charging scheme before transitioning into constant voltage charging.

Internal Resistance (Maximum)

This is the resistance within the battery, generally different for charging and discharging.

Basic Battery Terminology

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There are certain  basic battery terminology that tends to be misunderstood in practice. These terms commonly refers to the condition of the battery as well as capacity of the battery:

State of Charge (SOC) %

SOC defines the present battery capacity as a percentage of maximum capacity. SOC is generally calculated using current integration to determine the change in battery capacity over time.

Depth of Discharge (DOD) %

This expresses the percentage of battery capacity that has been discharged expressed as a percentage of maximum capacity. A discharge to at least 80 % DOD is referred to as a deep discharge.

Terminal Voltage (V)

This is the voltage between the battery terminals with load applied. Terminal voltage varies with SOC and discharge/charge current.

Open Circuit Voltage (V)

This is the voltage between the battery terminals with no load applied. The open-circuit voltage depends on the battery state of charge (SOC), increasing with state of charge.

Internal Resistance

This is the resistance within the battery, generally different for charging and discharging, also dependent on the battery state of charge. As internal resistance increases, the battery efficiency decreases and thermal stability is reduced as more of the charging energy is converted into heat.

Consider the battery circuit above, where E is the open circuit voltage, I is the load current flowing in amps, V is the terminal voltage across a load resistance $R_L$, r is the battery internal resistance

Power  input to battery is given by: $$P_i = IE$$ $$E = I (R+r)$$ $$P_i = I *I(R+r) = I^2(R+r)$$ power output: $$P_o = IV = I*IR = I^2R$$ Battery Efficiency  $$Eff = {\frac{P_o}{P_i}} = {\frac{I^2R}{ I^2(R+r)}} = {\frac{R}{(R+r)}}$$ As can be seen, the more the internal resistance of the battery, the less efficient the battery becomes due to increasing conversion of useful battery energy to heat.

C and E – Rates

In describing batteries, discharge current is often expressed as a C-rate in order to normalize against battery capacity, which is often very different between batteries. A C-rate is a measure of the rate at which a battery is discharged relative to its maximum capacity.

C – Rate can be expressed as:

$$I = M * C_n $$     

Where:

I  = Discharge current in Amps

C = Numerical value of rated capacity of the battery in ampere – hours (AH)

n = Time in hours for which rated capacity of battery is declared

M = Multiple or fraction of C

Consider a battery rated at 200AH with a discharge current of 10Amps, the C rate is calculated as: 

M = I/Cn  = 10/200 = 1/20 = 0.05C or C/20 rate

E’’ Rate

An E-rate describes the discharge power. A 1E rate is the discharge power to discharge the entire battery in 1 hour. Just like the C rate, the E rate can be expressed as:

$$P = M * E_n $$    

Where:

I  = Discharge current in Amps

E = Numerical value of rated power of the battery in watt – hours (Wh)

n = Time in hours at which the battery was rated

M = Multiple or fraction of C

Consider a battery with rated at 1200mWh with rated power of 600mW, the E rate is calculated as :

M = P/En  = 600mW/1200mW  = 0.5E or E/2 rate

Basics of Battery Capacity Ratings

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With the rise in global warming due to excessive use of fossil fuels on the plant, calls are becoming increasingly louder for renewable energy sources that are less damaging to the environment and sustainable in the long run. Batteries are a common feature of renewable energy sources such as solar systems as well as a common feature in both cars using fossil fuel derivatives and electric cars which are being touted to replace fossil fuel cars in the feature.

Given the role batteries play in our everyday life, there is the need to understand battery capacity ratings which are commonly used.

What is the Capacity of a Battery?

Battery capacity is the amount of electrical energy a battery can deliver when fully charged. The capacity of a battery is determined by factors such as size, number of plates, the number of cells and the strength and volume of electrolyte.

Common battery capacity ratings in use are:

1. Cold Cranking Amperes (CCA)

2. Reserve Capacity (RC)

3. Amp-Hours (AH)

4. Power (Watts)

Cold Cranking Amperes (CCA)

This capacity rating applies to the ability of the battery to provide the required energy to drive a prime mover e.g. car engine. In this case, it refers to the ability of the battery to provide energy to crank an engine during starting. This will entail a large discharge in a short time. The CCA rating of a battery specifies in amperes the discharge load a fully charged battery at 0°F can deliver for 30 seconds while maintaining a voltage of at least 1.2 volts per cell 

Reserve Capacity (RC)

This describes the ability of a battery to provide emergency energy for a given time to meet certain load demands should the battery charging system fails. This will require adequate battery capacity at normal temperatures for certain period of time.  The RC rating of a battery specifies in minutes, the length of time a fully charged battery at 80°F (26.7°C) can be discharged at 25 Amps while maintaining a voltage of at least 1.75 volts per cell

Amp-Hours (AH)

The Amp-Hour (AH) rating of a battery is the most popular and commonly used rating of a battery. It is often called the 20-hour discharge rating. The Amp-Hour rating of a battery specifies in amp-hours, the current the battery can provide in 20 hours at 80°F (26.7°C) while maintaining a voltage of at least 1.75 volts per cell.

Amp-Hour (AH) = Current x Time (Hours)

A battery that delivers 10Amps for 20hrs has a capacity of = 10 x 20 = 200AH.

Power (Watts)

For prime mover applications where the power is required to provide cranking power, its capacity can also be rated in watts. The power rating of a battery in watt is determined by multiplying the current available by the battery voltage at 0°F (-17.8°C)

How to Calculate the Inductance of an Electric Cable

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The inductance, L , per core of a 3-core cable or of three single-core cables comprises two parts namely the self-inductance of the conductor and the mutual inductance with other cores. 

The formula for calculating the Inductance of a cable is given by:

$L = K + 0.2Log_e{\frac{2S}{d}}$                    (Hm/Km)

Where:
L  =  Inductance of cable in (Hm/Km)

K  =  a constant relating to the conductor formation (see table below)

S  =  axial spacing between conductors within the cable (mm) or axial spacing between 

       Conductors of a trefoil group of single core cables (mm) or 

   =  1.26 x phase spacing for a flat formation of three single-core cables (mm)

d =  conductor diameter or for shaped designs the diameter of an equivalent circular     

        conductor (mm)

For 2-core, 3-core and 4-core cables, the inductance obtained from the formula should be multiplied by 1.02 if the conductors are circular or sector-shaped, and by 0.97 for 3-core oval conductors.

Typical Values for K for Different Stranded Conductors (at 50Hz)

Number of Wires in Conductor	K
3	0.0778
9	0.0642
7	0.0554
37	0.0528
61 and Over	0.0514
1 (Solid)	0.0500
Hollow core conductor, 12mm duct	0.0383

Electrical and Physical Properties of Common Metals Used in Manufacturing Cables

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The tables below indicate the electrical and physical properties of metals commonly used in the manufacture of electric cables in the electrical industry. Familiarity with these properties is required to fully grasp the key advantages and disadvantages of the various materials used and to understand from a practical standpoint why they are applied in the area they are used.

Electrical Properties

The table below indicates the electrical properties of the common metals used in cables. Taking price into consideration the below listed properties, Copper and Aluminium are clearly the best choice for conductors the manufacture of all manner of electric cables although there has been experimentation with other metals for example Sodium in certain applications:

Metals	Relative Conductivity (Copper = 100)	Electrical Resistivity at 20°C (Ωm, 10-8)	Temperature Coefficient of Resistance (per °C)
Silver	106	1.626	0.0041
Copper (HC, anealed)	100	1.724	0.0039
Copper (HC, Hard drawn)	97	1.777	0.0039
Tinned Copper	95 - 99	1.741 - 1.814	0.0039
Aluminium (EC grade, Soft)	61	2.803	0.0040
Aluminium (EC grade,         1/2H - H)	61	2.826	0.0040
Sodium	35	4.926	0.0054
Mild Steel	12	13.80	0.0045
Lead	8	21.4	0.0040

Physical Properties of Metals Used in Electric Cables
The physical properties of metals used for conductors and sheaths are given in the table below:

Property	Unit	Aluminium	Copper	Lead
Density at 20°C	Kg/m3	8890	2703	11370
Coefficient of thermal expansion per °C	x 10-6	17	23	29
Melting point	oC	1083	659	327
Thermal Conductivity	W/cm oC	3.8	2.4	0.34
Ultimate Tensile Stress
Soft temper	MN/m2	225	70 - 90	-
3/4H to H	MN/m2	385	125 - 205	-
Elastic Modulus	MN/m2	26	14	-
Hardness
Soft	DPHN	50	20 - 25	5
3/4H to H	DPHN	115	30 - 40	-
Stress Fatigue Endurance Limit (Approximate)	MN/m2	±65	±40	±2.8

Except for conductors of self-supporting overhead cables, Copper is invariably used in the annealed condition. Solid Aluminium conductors are also mainly used in a soft condition but stranded Aluminium conductors are 3H (hard) to H. Aluminium sheaths are now extruded directly onto cables and hence of soft temper but a small amount of work hardening occurs during corrugation.

Basics of Electrical Lighting Design I

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As you may already know, Light is that part of the electromagnetic spectrum that is perceived by our eyes. There are some basic parameters that are used in the design of lighting systems that must be understood before they are used. They are:

• Luminous Flux (Փ)


• Luminous Efficiency


• Luminous Intensity (I)


• Illuminance (E)


• Luminance (L)

Luminous Flux (Փ)
The luminous flux describes the quantity of light emitted by a light source.
It is commonly represented by the symbol, Փ. Its unit of measurement is the lumen (lm)

Luminous Efficiency
The luminous efficiency of an electrical lamp is the ratio of the luminous
flux emitted by the lamp to the electrical power consumed by the lamp. Its unit is (lm/W).
It is a measure of a lamp’s economic efficiency.

Luminous Intensity (I)
The luminous intensity describes the quantity of light that is radiated in a particular
Direction from a light source such as a lamp. This is a useful measurement for directive lighting elements such as reflectors. In lighting design, it is represented by the symbol, I. Its unit of measurement is the candela (cd).
Luminous Intensity is given by:
I = Փ/W
W = Electrical power consumed by lamp

Illuminance (E)
Illuminance describes the quantity of luminous flux falling on a surface. It decreases by the square of the distance (inverse square law). Lighting standards usually specify the required illuminance for indoor work places and industrial areas. It is represent by the symbol, E. Its unit of measurement is the lux or lx.

Illuminance is given by:
E (lx) = luminous flux(lm)/area (m2) = Փ/A . Note that lx = lm/m2

Luminance (L)
Luminance specifies the brightness of a surface and is essentially dependent on its reflectance (finish and colour). It is the only basic lighting parameter that is perceived by the eye. It is represented by the symbol, L. Its unit of measurement is cd/m2.

Luminance is given by:
L = I/A or L = E/W.
W = Electrical power consumed by lamp

Lamp Characteristics Required to Specify an Electrical Lamp

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Electrical lamps possess different characteristics that make them suitable for specific applications. To be able to specify the right lamp for the best application, the following lamp characteristics need to be understood:

Lamp Electrical Power

This is the electrical power consumption of the lamp as opposed to the power consumption of a system comprising lamp and ballast.

Luminous Flux/Luminous Efficiency

The luminous flux specifies the total amount of light generated by a lamp. The rated luminous flux is usually measured at a standardised measurement temperature of 25 °C in units of lumen [lm]. The ratio of luminous flux to electrical power consumption gives the luminous efficiency [lm/W]. The system luminous efficiency also includes the power consumption of the ballast.

Service Life

The average service life is normally specified, being the time by which statistically half the lamps are still working (mortality). The drop in luminous flux also needs to be taken into account.

Light Colour

The light colour describes the colour impression made by a white light source as relatively warm (ww = warm) or relatively cool (nw = intermediate, tw = cool). It is affected by the red and blue colour components in the spectrum. The typical light colors are tabulated below:

Designation	Colour Temperature	Appearance	Association
ww	Up to 3,300K	Reddish	Warm
nw	3,300K to 5,300K	White	Intermediate
tw	Above 5,300K	Blue-ish	Cool

Colour Rendition

The spectral components of the light determine how well various object colours can be reproduced. The higher the colour rendition index (CRI), or the lower the colour rendition group number, the better the colour rendition in comparison with the optimum reference light.

Warm-up time

Discharge lamps in particular need between 30 seconds and several minutes to warm up and output the full luminous flux. This is a critical consideration in the selection of discharge lamps for a given application.

Re-Start Time

High-pressure discharge lamps need to cool down for several minutes before they can be started again. This needs to be considered for the particular installation where the discharge lamps are required to be used.

Dimming Capability of Lamp

Apart from incandescent and halogen incandescent lamps, nowadays all fluorescent and compact fluorescent lamps can also be dimmed over almost any range. Metal halide lamps, however, are still not approved by the manufacturers for dimming, because this may have uncontrollable effects on light quality and lamp service life. The power of high pressure sodium- and mercury-vapour lamps can be varied, but only in discrete levels.

Burning Position

Manufacturers specify the permitted burning positions for their lamps. For some metal halide lamps, only certain burning positions are allowed so as to avoid unstable operating states. Compact fluorescent lamps may usually be used in any burning position, although important properties such as the luminous flux vs. temperature curve may vary with position.